Question

A triangle has sides A,B, and C. If the angle between sides A and B is `(3pi)/8`, the angle between sides B and C is `pi/4`, and the length of B is 7, what is the area of the triangle?

Answer 1

≈ 17.32 square units

Explanation:

The area of a triangle can be calculated using `1/2ab sintheta`
where `theta" is the angle between a and b "`

In this triangle , only know the length of one side B. Require to find the length of A or C.

This can be done using the`color(blue)" sine rule "`

`A/sinA = B/sinB = C/sinC`
where the angles A , B and C on the denominator represent the angles opposite the corresponding sides A , B and C.

`color(red)" Calculating the length of side C"`

using `B/sinB = C/sinC`

Before using this, require the size of angle B

The sum of the 3 angles in a triangle `= pi`

angle B `= [pi - ((3pi)/8 + pi/4 )] = pi - (5pi)/8 = (3pi)/8`

Now angle B = angle C hence side B = sideC = 7

In this question B = C = 7 and `theta = pi/4`

`"area" = 1/2xxBxxCsintheta = 1/2xx7xx7xxsin(pi/4) ≈ 17.32`